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United States Patent |
6,032,531
|
Roszhart
|
March 7, 2000
|
Micromachined acceleration and coriolis sensor
Abstract
A solid state silicon micromachined acceleration and Coriolis (MAC) sensor
that measures linear and angular motion. The MAC sensor is a single device
that performs the functions of a conventional accelerometer and a
gyroscope simultaneously. The MAC sensor is unique in that it is a
differential dual stage device using only one micromachined proof mass to
measure both linear and angular motions. The single proof mass is
connected to opposing electromechanical resonators in a monolithic
microstructure made from single crystal silicon. This unique design offers
improvements in measurement performance and reductions in fabrication
complexity that are beyond the state the art of earlier micromachined
inertial sensors.
Inventors:
|
Roszhart; Terry V. (West Paterson, NJ)
|
Assignee:
|
Kearfott Guidance & Navigation Corporation (Wayne, NJ)
|
Appl. No.:
|
906218 |
Filed:
|
August 4, 1997 |
Current U.S. Class: |
73/504.04; 73/514.15; 73/514.29 |
Intern'l Class: |
G01C 019/00; G01P 015/10; 514.34; 514.35 |
Field of Search: |
73/504.02,504.03,504.04,504.12,504.14,504.15,514.02,514.15,514.16,514.29
|
References Cited
U.S. Patent Documents
3614678 | Oct., 1971 | Engeler et al.
| |
4230953 | Oct., 1980 | Wilcox.
| |
4488131 | Dec., 1984 | Griffin et al.
| |
4945765 | Aug., 1990 | Roszhart.
| |
5001933 | Mar., 1991 | Brand.
| |
5018858 | May., 1991 | Malvern.
| |
5203208 | Apr., 1993 | Bernstein | 73/504.
|
5261277 | Nov., 1993 | Thomas et al. | 73/514.
|
5315874 | May., 1994 | Petrovich et al.
| |
5334901 | Aug., 1994 | Albert et al.
| |
5341682 | Aug., 1994 | Hulsing, II.
| |
5349316 | Sep., 1994 | Sterns.
| |
5396798 | Mar., 1995 | Frische | 73/514.
|
5627316 | May., 1997 | De Winter et al. | 73/514.
|
5656778 | Aug., 1997 | Roszhart | 73/504.
|
Primary Examiner: Williams; Hezron
Assistant Examiner: Kwok; Helen C.
Attorney, Agent or Firm: Klauber & Jackson
Claims
What is claimed is:
1. A micromachined sensor for measuring linear and angular motion, said
sensor comprising:
a generally planar substrate, wherein said substrate is generally aligned
in a wafer plane defined by a first axis and a second axis, wherein said
second axis is orthogonal to said first axis, wherein said substrate is
generally perpendicular to a third axis which is orthogonal to said wafer
plane, and wherein said substrate is formed to include:
a frame having an inner cavity;
a proof mass disposed in said inner cavity, said proof mass having a top
surface and a bottom surface;
flexural support means for connecting said proof mass to said frame and
suspending said proof mass within said cavity; and
a plurality of resonators, including at least two opposite resonators which
are disposed on opposite sides of said proof mass;
excitation means for vibrating said proof mass at a dither frequency;
sensing means for sensing the vibration of said resonators; and
means for mounting said excitation means and said sensing means adjacent
said proof mass;
wherein said proof mass is capable of vibrating outside said wafer plane;
whereby said proof mass is capable of applying linear acceleration and
rotational Coriolis forces, or displacements caused thereby, to said
resonators in response to linear and angular motion of said sensor.
2. The sensor according to claim 1 wherein said plurality of resonators
further comprises at least two offset resonators which are disposed on
different planes, said different planes being generally parallel to said
wafer plane.
3. The sensor according to claim 1 wherein plurality of resonators further
comprises at least two coplanar resonators.
4. The sensor according to claim 1 wherein linear movement of said sensor
along said third axis causes said proof mass to modulate resonant
frequencies of said resonators, wherein a vibration frequency around a
natural resonant frequency of one of said resonators increases while a
vibration frequency around a natural resonant frequency of an opposite
resonator decreases, and wherein the difference in vibrational frequency
around the natural resonant frequency between said resonators is
proportional to a translation of said sensor along said third axis.
5. The sensor according to claim 1 wherein rotational movement of said
sensor about said third axis creates Coriolis forces which induce an
oscillating torque on said proof mass about said first axis, thereby
causing said proof mass to modulate a vibration frequency of said
resonators, wherein the vibration frequency of a first resonator is
increased while the vibration frequency of a second resonator decreases,
wherein the difference in vibration frequency of said first and second
resonators is proportional to a rotation rate of said sensor about said
third axis.
6. The sensor according to claim 1 wherein said means for vibrating said
proof mass further comprises means for rotationally dithering said proof
mass about said second axis at said dither frequency.
7. The sensor according to claim 1 wherein said plurality of resonators
further comprises:
a first resonator disposed proximate said top surface of said proof mass
and generally along said second axis; and
a second resonator disposed proximate said bottom surface of said proof
mass and generally along said second axis.
8. The sensor according to claim 1 wherein the natural resonant frequencies
of said resonators are substantially equal.
9. The sensor according to claim 1 wherein said mounting means further
comprises a pair of caps, each cap having an inner surface and an outer
surface, wherein said inner surface is provided with a well, wherein said
generally planar substrate is disposed between said caps and attached
thereto, and wherein said wells are adapted to allow said proof mass to
vibrate outside said wafer plane.
10. The sensor according to claim 9 wherein said means for vibrating said
proof mass further comprises:
a plurality of electrodes disposed in at least one of said wells and
adjacent said proof mass, said plurality of electrodes including at least
one proof mass driver electrode for providing electrostatic forces to said
proof mass thereby causing said proof mass to vibrate at said dither
frequency;
electronic circuitry, connected to said plurality of electrodes, for
exciting said plurality of electrodes and for sensing modulations in
vibration frequencies of said plurality of resonators caused by the linear
acceleration and rotational Coriolis forces so as to produce acceleration
and rotation signals indicative of the linear and angular motion of said
sensor; and
means for connecting said electronic circuitry to said plurality of
electrodes.
11. The sensor according to claim 10 wherein said plurality of electrodes
further comprise a plurality of proof mass balance electrodes.
12. The sensor according to claim 11 wherein said balance electrodes
further comprise a plurality of diagonal balance electrodes.
13. The sensor according to claim 10 further comprising means for damping
proof mass resonance about said first axis in order to improve dynamic
response.
14. The sensor according to claim 13 wherein said proof mass resonance
damping means further comprises means for applying an oscillating voltage
to said electrodes.
15. The sensor according to claim 10 wherein said at least one driver
electrode rotationally dithers said proof mass about said second axis at
said dither frequency.
16. The sensor according to claim 10 wherein said means for connecting said
electronic circuitry to said plurality of electrodes further comprises at
least one electroplated feedthrough hole disposed through at least one of
said caps; and wherein said feedthrough hole is adapted to supply
electrical energy to said electrodes.
17. The sensor according to claim 1 wherein at least one of said resonators
further comprises a cantilever beam having a proximal end attached to said
proof mass and a free distal end extending into said cavity.
18. The sensor according to claim 1 wherein a vibration frequency
corresponding to a linear movement is modulated about a frequency which
differs from said dither frequency.
19. The sensor according to claim 1 further comprising means for decoupling
resonator modes of opposed said resonators.
20. The sensor according to claim 1 wherein at least two of said resonators
have a frequency mismatch.
21. The sensor according to claim 1 wherein said sensor is adapted to
exhibit a diagonal inertia tensor, equal rotational frequencies.
22. The sensor according to claim 1 wherein said flexural support means
further comprises a first plurality of opposed flexural supports generally
disposed in a first plane, wherein said first plane is generally parallel
to said wafer plane.
23. The sensor according to claim 22 wherein said flexural support means
further comprises a second plurality of opposed flexural supports
generally disposed in a second plane, wherein said second plane is
generally parallel to said wafer plane, and wherein said second plane is
offset from said first plane.
24. The sensor according to claim 23 wherein said flexural support means
further comprises a plurality of diagonally opposed flexural supports.
25. The sensor according to claim 24 wherein said diagonally opposed
flexural supports further comprises four supports.
26. The sensor according to claim 24 wherein said diagonally opposed
flexural supports further comprises eight supports.
27. The sensor according to claim 24 wherein said diagonally opposed
flexural supports are coplanar.
28. The sensor according to claim 1 further comprising at least one body
attached to said proof mass, whereby the mass and at least one moment of
inertia of said proof mass is increased.
29. The sensor according to claim 28 wherein said body is bonded to said
proof mass.
30. The sensor according to claim 28 wherein said body further comprises at
least two opposing bodies attached to opposite sides of said proof mass.
31. The sensor according to claim 28 wherein said body is generally
spherical.
32. The sensor according to claim 28 wherein said means for mounting said
excitation means and said sensing means adjacent said proof mass further
comprises at least one throughhole adapted to allow at least a portion of
said body to extend therethrough.
33. The sensor according to claim 10 wherein said electronic circuitry
further comprises a proof mass oscillator for exciting said proof mass
through said plurality of electrodes.
34. The sensor according to claim 33 wherein said proof mass oscillator
senses a first natural resonant frequency of said proof mass and provides
a reference frequency output relating thereto.
35. The sensor according to claim 10 wherein said electronic circuitry
further comprises resonator oscillator means for exciting said resonators.
36. The sensor according to claim 35 wherein said resonator oscillator
means sense modulations in said plurality of resonators and provides
frequency modulated outputs related thereto.
37. The sensor according to claim 36 wherein said electronic circuitry
further comprises demodulators for processing said frequency modulated
outputs and for providing linear acceleration signals and rotational
velocity signals.
38. The sensor according to claim 37 wherein said electronic circuitry
further comprises a differential synchronous detector for processing said
rotational velocity signals and for providing differential rotational
velocity signals.
39. The sensor according to claim 37 wherein said electronic circuitry
further comprises a differential frequency counter for processing said
linear acceleration signals and for providing differential linear
acceleration signals.
Description
FIELD OF THE INVENTION
The present invention relates generally to linear and angular motion
sensors and, more particularly, to a solid state silicon micromachined
acceleration and Coriolis sensor that measures linear and angular motion.
DESCRIPTION OF THE PRIOR ART
Previous attempts to develop inertial multisensors can be divided into
three general categories. The first of these consists of a triad of
accelerometers that are dithered about a common axis using a rotational or
flexural mechanism. Since at least three accelerometers are being
oscillated simultaneously, this approach usually requires the most volume
and power. This method is not monolithic and considerable complexity of
design is needed to make electrical contact with the individual vibrating
accelerometers.
There is a second approach that uses two oppositely vibrating proof masses
and two magnetically driven resonators to sense both rotational and linear
motion. This approach uses a monolithic structure that controls the dither
motion and the Coriolis response of the proof masses as well as the
vibrational motion of the resonators. Since there are two proof masses, a
mechanical "phase link" is also needed to assure anti-parallel proof mass
motion. The monolithic nature of this structure is advantageous in
relation to the benefits of batch micromachining methods but the
integration of two proof masses in one sensor greatly increases the design
complexity. This increased complexity imposes design limits that effect
sensor performance and fosters a multitude of unwanted parasitic
vibrational modes that impair measurement accuracy. The need for two proof
masses also increases sensor power and volume.
A third category of devices consists of micromachined structures that
exhibit two modes of vibration that are orthogonally oriented. As the
device rotates about its sensitive axis, vibrations in one mode are
coupled into the dual orthogonal mode. Measurements of the device rotation
can then be made by sensing the magnitude of the vibration occurring in
this second mode. Unfortunately, this second mode operates at the same
frequency as the first mode. This means that small perturbations in mode
orthogonality, fabrication tolerances, or electrical cross talk can also
couple energy between modes. This produces an error signal that appears as
a false rotation and reduces the accuracy of this type of sensor. In
addition, this type of sensor is often insensitive to linear acceleration
and cannot measure rotational and linear motions simultaneously.
SUMMARY OF THE INVENTION
The present invention contemplates a solid state silicon micromachined
acceleration and Coriolis (MAC) sensor that measures linear and angular
motion. The MAC sensor is a single device that performs the functions of a
conventional accelerometer and a gyroscope simultaneously. Thus the MAC
sensor can be used as a motion control sensor in military or commercial
settings. One application is in miniature inertial guidance and navigation
systems where issues of size, weight, performance, and cost are important.
The MAC sensor is unique in that it is a differential dual stage device
using only one micromachined proof mass to measure both linear and angular
motions. The single proof mass is connected to opposing electromechanical
resonators in a monolithic microstructure made from single crystal
silicon. This unique design offers improvements in measurement performance
and reductions in fabrication complexity that are beyond the state the art
of earlier micromachined inertial sensors.
The MAC sensor retains all of the advantages of earlier types of solid
state sensors. The MAC sensor has no rotating parts and its motion sensing
assembly does not have any of the material interfaces or joints that
contribute to measurement errors. It can be fabricated from existing
micromachining processes and offers the economies of size, weight, and
cost that are typical of the integrated circuit industry.
Since the MAC sensor can measure both linear and angular motions, only
three MAC sensor chips are needed for a full six axis inertial measurement
instrument. Alternate configurations are possible that can provide four
and even six axes of measurement on a single chip. As a result, the MAC
sensor has the potential to establish a new generation of motion sensors
that are small, inexpensive, rugged, and well suited to many applications,
including advanced inertial guidance and navigations systems and other
applications which required high levels of performance.
Accordingly, the primary objective of the present invention is to provide a
solid state silicon micromachined acceleration and Coriolis (MAC) sensor
that measures linear and angular motion.
Other objectives and advantages of the present invention will become
apparent to those skilled in the art upon reading the following detailed
description and claims, in conjunction with the accompanying drawings
which are appended hereto.
BRIEF DESCRIPTION OF THE DRAWINGS
In order to facilitate a fuller understanding of the present invention,
reference is now being made to the appended drawings. The drawings should
not be construed as limiting the present invention, but are intended to be
exemplary only.
FIG. 1A is a top perspective view of a monolithic electromechanical
structure of a solid state silicon micromachined acceleration and Coriolis
(MAC) sensor according to a first embodiment of the present invention.
FIG. 1B is a bottom perspective view of the monolithic electromechanical
structure shown in FIG. 1A.
FIG. 2 is an exploded top perspective view of a solid state silicon
micromachined acceleration and Coriolis (MAC) sensor chip assembly
according to a first embodiment of the present invention.
FIG. 3 is an exploded top perspective view of an electronic signal
processing system for a solid state silicon micromachined acceleration and
Coriolis (MAC) sensor according to the present invention.
FIG. 4A is a top perspective view of a monolithic electromechanical
structure of a four axis solid state silicon micromachined acceleration
and Coriolis (MAC) sensor according to an alternate configuration of a
first embodiment of the present invention.
FIG. 4B is a bottom perspective view of the monolithic electromechanical
structure shown in FIG. 4A.
FIG. 5A is a top perspective view of a monolithic electromechanical
structure of a six axis solid state silicon micromachined acceleration and
Coriolis (MAC) sensor according to another alternate configuration of the
first embodiment of the present invention.
FIG. 5B is a bottom perspective view of the monolithic electromechanical
structure shown in FIG. 5A.
FIG. 6 is an exploded perspective view of a sensor chip assembly according
to a second embodiment of the present invention.
FIG. 7 is a top view of another configuration of the second embodiment of
the present invention, shown without a top cap.
FIG. 8 is a side view of the sensor of FIG. 7 showing a top cap, a silicon
device layer, and a bottom cap.
FIG. 9 is an end view of the sensor of FIG. 7 showing a top cap, a silicon
device layer, and a bottom cap.
FIG. 10 is a perspective view of a proof mass, a pair of offset opposing
resonators, eight flexure supports, and two microspheres, according to the
second embodiment of the present invention.
FIG. 11 illustrates the forces and counterforces produced by linear
acceleration of the sensor in the z direction.
FIG. 12 illustrates the oscillating torque about the x axis created by
Coriolis forces produced by vibration of the proof mass about the y axis
and sensor substrate rotations about the z axis.
FIG. 13 illustrates cross-axis coupling of the y axis dither motion into
the x output axis as created by the rotationally induced Coriolis forces,
shown by equivalent mass and moment representation.
FIG. 14 illustrates a dither drive system for oscillating at the natural
resonant frequency of the y axis.
FIG. 15 is a top view of a substrate, having a four flexure/low band
resonator configuration, according to the second embodiment of the present
invention.
FIG. 16 is a top view of a substrate, having a four flexure/high band
resonator configuration, according to the second embodiment of the present
invention.
FIG. 17 is a top view of a substrate, having an eight flexure
configuration, according to the second embodiment of the present
invention.
FIG. 18 is a top view of a substrate, having a coplanar flexure/single
microsphere configuration, according to the second embodiment of the
present invention.
DETAILED DESCRIPTION OF THE PRESENT INVENTION
A first embodiment and various alternate configurations thereof are
presented in FIGS. 1A-5B. A second embodiment and various alternate
configurations thereof are presented in FIGS. 6-18.
I. Mechanical Design of a First Embodiment
The elements of a micromachined acceleration and Coriolis (MAC) sensor
according to a first embodiment of the present invention are shown in
FIGS. 1-3. A monolithic electromechanical structure that is the central
feature of the MAC sensor is shown in FIG. 1. This structure performs all
the mechanical functions of the sensor. This structure is bonded into a
microchip assembly that is connected to an electronic signal processing
system. The details of the first embodiment of the MAC sensor microchip
are shown in FIG. 2, and an electronic signal processing system is shown
in FIG. 3.
A. Chip Design
The electromechanical structure that is central to the first embodiment of
the MAC sensor chip consists of a frame like substrate 1, a vibrating mass
2, two flexural resonators 3 and 4, and four flexural supports 8, 9, 10,
and 11. This is a monolithic structure that can be formed in single
crystal silicon wafers using established microlithography and
micromachining techniques.
This structure is further described with respect to the right handed xyz
coordinate system shown in FIG. 1. The proof mass 2 is driven by
electrostatic forces that cause it to vibrate in the direction 5 that is
coincident with the x axis. The flexural resonators 3 and 4 are oriented
along the z axis. It is shown later that the rotation sensitive axis of
this sensor is perpendicular to these directions and lies along the vector
6 coincident with the y axis. The acceleration sensitivity of the sensor
is located along the z axis.
The silicon structure of FIG. 1 is bonded to two Pyrex glass or silicon
caps 24 and 25 that are shown in FIG. 2. Both of these caps have proof
mass wells 26 that are etched into the caps' surfaces. These wells are
recessed an amount sufficient to allow for the vibrational motion of the
proof mass perpendicular to the xy plane. The wells also contain metallic
electrode patterns that are used to vibrate the proof mass 2 and the
resonators 3 and 4. Electroplated feedthrough holes 35 are formed in the
caps to make electrical contact to the inside of the chip. These
feedthroughs have topside electrode patterns that can be used for wire
bonding.
The caps are also fabricated from wafers and are bonded to the center
silicon wafer before being diced into the rectangular chips. This makes it
possible to use batch fabrication methods that permit the manufacturing of
all the individual sensors on a single wafer assembly at one time. This
greatly reduces the labor and cost of these devices.
B. Electronics Design
The microchip of the first embodiment shown in FIG. 2 is die bonded into a
vacuum tight hybrid package and connected to the electronic signal
processing system shown in FIG. 3. Item 12 represents an electronic
oscillator that is used to drive the proof mass 2 at its resonant
frequency. This is done through the metallic electrodes that are located
on the microchip caps. This oscillator also provides a reference frequency
19 that is used by the signal electronics for synchronous detection of
demodulated output signals 20 and 22, as will be described more fully
below.
Items 13 and 14 are additional oscillators that are used to drive the
individual flexural resonators 3 and 4. These resonators have natural
resonant frequencies that are approximately equal and are much greater
than the natural frequency of the proof mass. It is shown below that the
frequencies of the resonators are modulated by the linear acceleration and
Coriolis forces produced by the proof mass. This process is known as
heterodyning or frequency modulation.
The frequency modulated output of each of these oscillators is sent to
their respective demodulators, items 15 and 16, where the resonators'
average frequencies are removed from the signals. The output of the
demodulators is then sent to two dual stage detectors 17 and 18 to produce
outputs that are proportional to linear acceleration and rotational
velocity.
It is important to note that the resonators 3 and 4 have been placed at
opposite ends of proof mass 2. This was done so that the acceleration and
Coriolis forces applied to each resonator are equal in magnitude and
opposite in sign. When the signals from each channel of the MAC sensor
electronics are combined at the dual stage detectors 17 and 18, the parts
of the signals that are proportional to each acceleration and rotation
signal are added (to double the sensitivity) and the common mode parts are
subtracted (to reduce measurement errors). The outputs 27 and 28 are,
therefore, true differential signals that are proportional to the linear
acceleration and angular rotational velocity that are applied to the
sensor chip.
II. Principles of Operation of the First Embodiment
The micromachined acceleration and Coriolis (MAC) sensor is a highly
integrated device that provides for the simultaneous, differential
measurement of linear and angular motion using only one monolithic proof
mass. Despite the multiplicity of functions, the MAC sensor offers a
structural simplicity that is not found in earlier sensors of the same
type. To explain its operation, the proof mass, resonator, and signal
detection subsystems will be described separately. In particular, the
propagation of the acceleration and rotational signals, as well as the
measurement errors, through the sensor system will be discussed.
A. Proof Mass Forces
1. Linear Acceleration
The prime function of the proof mass in the first embodiment is to apply
forces to the MAC resonators that are related to the inertial motion of
the sensor. One of these forces is produced by acceleration in the z
direction. When the substrate is accelerated along this axis, the inertia
of the proof mass produces a counterforce that is restrained by the
resonators at each end. According to Newton's law, the force produced by
linear acceleration is
F.sub.a =m.sub.pm a.sub.z (1)
wherein F.sub.a is the linear acceleration force, m.sub.pm is the mass of
the proof mass, and a.sub.z is the linear acceleration.
When the sensor is accelerated along the z axis, the proof mass produces a
force in resonator 3 that is tensile, and a force is resonator 4 that is
compressive.
2. Rotational Coriolis Force
The Coriolis "force" is actually an apparent acceleration attributed to a
body that is in motion with respect to a rotating coordinate system. If
the proof mass in the first embodiment shown in FIG. 1 is vibrating in the
direction 5, and, if the sensor substrate is rotating about the direction
6, then a Coriolis force will be produced in direction 7 which is
simultaneously perpendicular to both the velocity and rotation vectors.
This Coriolis force oscillates at the frequency of the proof mass and
modulates the natural resonant frequency of the two resonators 3 and 4.
Each of these resonators then produces a frequency modulated carrier
signal that is sensed by the signal processing electronics shown in FIG.
3.
The magnitude of the Coriolis force that is imposed on the proof mass in
the first embodiment is the cross product of the proof mass velocity
vector 5 and the coordinate rotation vector 6 and is given by
F.sub.c =2m.sub.pm .nu..OMEGA..sub.y (2)
wherein F.sub.c is the Coriolis force, v is the velocity of the proof mass,
and .OMEGA..sub.y is the inertial rotation velocity along the y-axis.
In order to evaluate this equation, it is necessary to compute the proof
mass velocity. Since the proof mass 2 is harmonically driven by the
oscillator 12, its equation of motion is given by
x=x.sub.pm sin ((.omega..sub.pm t) (3)
wherein x is the displacement of the proof mass, .omega..sub.pm is the
resonant frequency of the proof mass, and x.sub.pm is the displacement
magnitude of the proof mass. This equation is differentiated with respect
to time to give the proof mass velocity.
.nu.=.omega..sub.pm x.sub.pm cos (.omega..sub.pm t) (4)
This result can be substituted into equation (1) to give
F.sub.c =2m.sub.pm .omega..sub.pm .OMEGA..sub.y x.sub.pm cos
(.omega..sub.pm t) (5)
Equation (5) describes the magnitude of Coriolis force that is produced by
the vibrating proof mass 2. It is directed along the z direction and
oscillates at the frequency of the proof mass.
The Coriolis force in the first embodiment is applied to both of the two
resonators 3 and 4 that support the proof mass in the z direction.
Assuming that the flexure supports 8, 9, 10, and 11 offer negligible
stiffness in the z direction, then the force applied to the two resonators
is
##EQU1##
wherein F.sub.c3 is the Coriolis force applied to resonator 3, and
F.sub.c4 is the Coriolis force applied to resonator 4.
It should be noted that the resonators have been positioned so that the
Coriolis force that is applied to each resonator is equal in magnitude but
opposite in direction. For example, when resonator 3 is in tension,
resonator 4 is in compression.
B. Resonator Frequency Modulation
1. Signal Analysis
In the first embodiment, the resonators 3 and 4 are flexurally mounted
"beam like" structures that exhibit a natural mechanical resonance and a
sensitivity to in-plane (z axis) mechanical forces. In the absence of an
in-plane force each resonator vibrates at a natural resonance determined
by the mass and stiffness of the structure. When an in-plane force is
applied to the resonator, the frequency is changed at a rate that depends
upon the buckling load of the structure. In particular, if the applied
force is tensile, then the resonator's frequency increases. If the force
is compressive, the frequency decreases. This frequency response is given
by
.omega.=.omega..sub.o +k.sub.1 F.sub.T +k.sub.2 F.sub.T.sup.2(8)
wherein .omega..sub.o is the natural frequency of the resonator, k.sub.1 is
the linear frequency scale factor, F.sub.T is the total net force applied
to the resonator along the z-axis, and k.sub.2 is the nonlinear frequency
scale factor.
The first term in this equation is the natural frequency of the resonator
and is determined by the mass and stiffness of the structure. The second
term of this equation, is the term that describes the force sensitivity of
the resonator. The last term shown in equation (8), accounts for the
nonlinearity of the resonator's force sensitivity. Additionally, higher
order terms are predicted by beam theory, but are usually small enough
that they can be ignored for most analyses.
The forces produced by the linear acceleration and rotational velocity are
given by equations (1), (6), and (7). Substituting these into equation (8)
gives
.omega.=.omega..sub.o +.DELTA..omega..sub.a (t)+.DELTA..omega..sub.c
(.omega..sub.pm)+.DELTA..omega..sub.n (2.omega..sub.pm) (9)
wherein .DELTA..omega..sub.a (t) is the frequency shift due to acceleration
and is equal to k.sub.1 m.sub.pm a.sub.z, .DELTA..omega..sub.c
(.omega..sub.pm) is the frequency shift due to rotation and is equal to
k.sub.1 2m.sub.pm .omega..sub.pm .OMEGA..sub.y x.sub.pm cos(.omega..sub.pm
t), and .DELTA..omega..sub.n (2.omega..sub.pm) is the frequency shift due
to nonlinearity and is equal to k.sub.2 (F.sub.a +F.sub.c).sup.2.
Equation (9) shows the explicit time dependence of the various terms. In
particular, the acceleration term and Coriolis term have separate time
dependencies which will allow their separation in the signal processing
scheme described later.
2. Error Analysis
The resonators are also sensitive to additional parameters that are not
part of the inertial motion to be measured. These additional parameters
contribute to the sensor's noise and could contribute to measurement
uncertainties. These error mechanisms are described by
.DELTA..omega..sub.e =.DELTA..omega..sub.T +.DELTA..omega..sub..epsilon.
.DELTA..omega..sub.g +.DELTA..omega..sub.s (10)
wherein .DELTA..omega..sub.e is the frequency shift due to errors,
.DELTA..omega..sub.T is the frequency shift due to temperature,
.DELTA..omega..sub..epsilon. is the frequency shift due to substrate
strain, .DELTA..omega..sub.g is the frequency shift due to electrostatic
gap changes, and .DELTA..omega..sub.s is the frequency shift due to
resonator strain.
The first term in equation (10) provides for the change in frequency caused
by changes in resonator temperature. For silicon this term is linear in
temperature and is defined by
.DELTA..omega..sub.T =.alpha..sub.T .omega..sub.o T (11)
wherein .alpha..sub.T is the temperature coefficient, and T is the
temperature.
Other resonator materials, such as quartz, exhibit nonlinear terms that are
too significant to ignore and would need to be included in this equation.
The second term in equation (10) describes the change in frequency caused
by strain in the sensor substrate. This strain can be caused by mounting
stress, by residual material stress generated during thermal fabrication
cycles and sensor chip assembly, or by general long term aging. In
particular, this term is defined by
.DELTA..omega..sub..epsilon. =k.sub.1 .epsilon..sub.s EA.sub.r(12)
wherein .epsilon..sub.s is the substrate strain, E is the modulus of
elasticity, and A.sub.r is the resonator cross sectional area.
Both equations (11) and (12) describe measurement errors that are
relatively independent of time and have, at most, a very slow time
variation.
The third term in equation (10) is an adjustment that must be made to
account for the change in the resonator's electrostatic gap that occurs
when the proof mass is oscillating in the x direction. Note that this term
is 90 degrees out of phase with the proof mass motion and will eventually
be eliminated by the signal processing electronics. This term is defined b
y
.DELTA..omega..sub.g =.chi.x sin (.omega..sub.pm t) (13)
wherein .chi. is the electrostatic gap coefficient.
The last term in equation (10) accounts for a frequency modulation that is
caused by stretching of the resonator when the proof mass moves in the x
direction. This motion produces a tension in the resonator that is tensile
for both directions of the x motion. As a result, the frequency shift
caused by resonator stretching is proportional to the square of the proof
mass displacement according to
.DELTA..omega..sub.s =.gamma.x.sup.2 =5.gamma.x.sub.pm.sup.2 (1-cos
2.omega..sub.pm t) (14)
wherein .gamma. is equal to k.sub.1 EA.sub.r /(2L.sup.2), and L is the
length of the resonator.
Note that this last term has a time independent part and a part that
oscillates at twice the proof mass frequency. This is because the
resonator stretching is proportional to the square of the proof mass
displacement.
3. Resonant Oscillator Analysis
Equations (9) and (10) can now be combined to analyze the response of each
resonator. Arbitrarily assigning resonator 3 to channel A and resonator 4
to channel B gives the following equations.
.omega..sub.A =.omega..sub.o +.DELTA..omega..sub.a (t)+.DELTA..omega..sub.c
(.omega..sub.pm)+.DELTA..omega..sub.n
(2.omega..sub.pm)+.DELTA..omega..sub.e (15)
.omega..sub.B =.omega..sub.o -.DELTA..omega..sub.a (t)-.DELTA..omega..sub.c
(.omega..sub.pm)+.DELTA..omega..sub.n
(2.omega..sub.pm)+.DELTA..omega..sub.e (16)
These equations describe the frequency output of each channel as modulated
by the linear acceleration, rotational velocity, and assorted error
mechanisms. The voltage outputs of each oscillator can also be determined.
In particular, the voltage output of channel A is given by
V.sub.A =V.sub.o (cos (.omega..sub.A +M.sub.1A cos (.omega..sub.pm
t)+M.sub.2 cos (.omega..sub.pm t))) (17)
wherein V.sub.o is the oscillator output voltage,
.omega..sub.A =.omega..sub.o -.DELTA..omega..sub.a (t)+.DELTA..omega..sub.n
(t)+.DELTA..omega..sub.T +.DELTA..omega..sub.68 (18)
M.sub.1A =M.sub.c +iM.sub.g (19)
##EQU2##
M.sub.2 =M.sub.n +M.sub.s (22)
##EQU3##
Similar equations are used for channel B, as follows
V.sub.B =V.sub.o (cos (.omega..sub.B +M.sub.1B cos (.omega..sub.pm
t)+M.sub.2 cos (.omega..sub.pm))) (25)
.omega..sub.B =.omega..sub.o -.DELTA..omega..sub.a (t)+.DELTA..omega..sub.n
(t)+.DELTA..omega..sub.T +.DELTA..omega..sub.68 (26)
M.sub.1B =-M.sub.c +M.sub.g (27)
Equations (15) through (27) now describe the output of both channels in
terms of the signal terms and error terms. Both channels are similar and
differ only in the signs that precede the signal terms. It is shown below,
that all error terms are canceled by the differential dual stage nature of
the MAC sensor geometry and electronic signal processing.
C. Signal Demodulation
Each of the resonators 3 and 4 are connected to their own oscillators 13
and 14. Each oscillator, in turn, is connected to one of two signal
processing paths which make up the separate channels of a dual stage
electronic system. Since each signal path is identical, the description of
the signal processing system can be covered by explaining one path only.
The oscillator 14 senses the instantaneous frequency of the resonator 3 and
provides a feedback signal of equal frequency and phase to maintain the
resonator's vibrational motion. This feedback signal can also be monitored
by the signal processing electronics to determine the resonator's
instantaneous frequency.
In normal operation, all indices of modulation (M) are maintained (by
design) at a value much less than unity. According to angular modulation
theory, the output of the oscillator can be divided into separate terms;
the carrier wave operating at the resonator's unmodulated frequency and
two sidebands operating at the sum and difference of the modulating
frequencies. This process, known as heterodyning, transforms a signal at a
low frequency (i.e., the proof mass frequency) into a band of frequencies
centered around the higher frequency of the resonator.
The oscillator output is detected in the demodulator circuit 16. This
circuit could be a phase locked loop (PLL) or another type of frequency
discriminator circuit. In either case, the function of the demodulator is
to identify the carrier frequency and separate it from the oscillator
output. The output of the demodulator is the carrier signal with the
frequency given by equation (18) for channel A and equation (26) for
channel B. This output contains the linear acceleration signal as well as
terms relating to the natural resonator frequency, thermal frequency
shift, residual strain effects, and offsets caused by resonator stretching
and nonlinearities.
The second output of the demodulator is a signal containing the time
dependent terms that originally modulated the resonator. This output is an
AC voltage given by
V'.sub.A =.alpha.G(M.sub.1A sin (.omega..sub.pm t)+M.sub.2 sin
(.omega..sub.pm t)) (28)
for channel A and by
V'.sub.B =.alpha.G(M.sub.1B sin (.omega..sub.pm t)+M.sub.2 sin
(.omega..sub.pm t)) (29)
for channel B wherein .alpha. is the frequency conversion coefficient
(volts/hertz), and G is the system gain (volt/volt). This output contains
the rotational velocity signal as well as error signals caused by gap
fluctuations and resonator stretching.
D. Dual Channel Detection
Equations (15), (16), (28), and (29) are the outputs of the resonators
after processing through both channels of the signal processing
electronics. One pair of these (equations 15 and 16) describe the signals
that are used to determine the sensor's linear acceleration. The remaining
pair (equations 28 and 29) provide the rotational velocity.
In particular, the linear frequency signals (eq. 14 and eq. 15) are
combined in the differential frequency counter 18. This circuit measures
the frequency of each of its inputs and provides an output that is the
difference of the inputs. This results in the linear output
.omega..sub.A -.omega..sub.B =2.DELTA..omega..sub.a (t)=2k.sub.1 m.sub.pm
a.sub.z (t)=.DELTA..omega. (30)
wherein
##EQU4##
This shows that the final output frequency is proportional to linear
acceleration. The common mode error terms caused by the resonator's
natural frequency, thermal shifts, residual stress, and resonator
stretching have been compensated by the differential function of the dual
channel counter 18.
The individual, single stage, Coriolis outputs of the MAC sensor are
connected together with the proof mass reference signal 19 at the dual
stage, synchronous detector 17. This circuit multiplies both Coriolis
outputs by the proof mass reference signal to remove the time dependent
cosine factors in equations (28) and (29). The only portions of these
signals that are coherent and in phase with the proof mass reference
signal are
V".sub.A =.alpha.G.DELTA..omega..sub.c (32)
V".sub.B =-.alpha.G.DELTA..omega..sub.c (33)
Due to the differential nature of detector 17, its final output is
.vertline.V".sub.A -V".sub.B
.vertline.=.vertline..DELTA.V".vertline.=2.alpha.G.vertline..DELTA..omega.
.sub.c .vertline.=2.alpha.G(2k.sub.1 m.sub.pm .omega..sub.pm x.sub.pm
.OMEGA..sub.y) (34)
This is a DC voltage that is proportional to the rotational velocity and
can be used to measure this quantity using
##EQU5##
wherein
.beta.=4.alpha.Gk.sub.1 m.sub.pm .omega..sub.pm x.sub.pm (36)
Once again, the differential function of this circuit has removed the error
terms that are not coherent with the proof mass. The result is a Coriolis
signal, the amplitude of which is proportional to rotational velocity and
is free of common mode errors.
Equations (31) and (35) describe the final outputs of the MAC sensor. These
equations are most accurate if resonators 3 and 4 are exactly identical
and exhibit the same resonant frequencies and sensitivities. If, due to
manufacturing tolerances and material variations, the resonators are not
ideally matched, then equations (31) and (35) could be expanded into
Taylor series that would use the frequencies or voltages of both stages.
These expanded formulas can accurately account for small differences in
resonator performance and can model the errors that would result from
these differences.
E. Performance Estimates of the First Embodiment
Estimates of the performance of the first embodiment of the MAC sensor can
be calculated from the preceding analysis. For example, Table 1 lists
values of MAC sensor parameters that are consistent with current
micromachining and electronic design practices.
TABLE 1
__________________________________________________________________________
PERFORMANCE ESTIMATES
SYMBOLS
VALUES
UNITS
__________________________________________________________________________
INERTIAL MOTION
LINEAR ACCELERATION a.sub.z
100 G
ROTATIONAL VELOCITY .OMEGA..sub.y
3.49 rad/sec
PROOF MASS
WIDTH .60 cm
LENGTH .60 cm
THICKNESS .05 cm
MASS m.sub.pm
.042 gm
RESONANT FREQUENCY .omega..sub.pm
31,400
rad/sec
DITHER AMPLITUDE x.sub.pm
1 microns
RESONATOR
NATURAL FREQUENCY .omega..sub.o
624,500
rad/sec
FORCE SENSITIVITY k.sub.1
16.90
rad/sec/dyne
SINGLE STAGE DEMODULATOR OUTPUT
REFERENCE VOLTAGE 5 volt
DEMODULATION COEFFICIENT
.alpha.
.0016
volt/(rad/sec)
SYSTEM GAIN G 200 volt/volt
DUAL STAGE SENSITIVITIES
LINEAR ACCELERATION 111 Hz/G
ROTATIONAL VELOCITY 1.42 volt/(rad/scc)
__________________________________________________________________________
These parameters predict a full scale acceleration output of 11.1 Khz at an
input of 100 G (19,600 cm/sec.sup.2). The rotational velocity output would
be 4.96 volts with an input of 200.degree./sec (3.49 rad/sec). This shows
that both the linear acceleration and the rotational velocity outputs
provided by the MAC sensor are reasonable in magnitude and can be easily
measured.
III. Unique Features of the First Embodiment
The micromachined acceleration and Coriolis sensor is a unique design that
has several inherent advantages. All of these features stem from the
geometry of the suspension system used to support the proof mass and
resonator within the sensor chip.
1. Single Proof Mass Design
The fact that only one proof mass is needed to produce differential outputs
for both linear and angular measurements offers several benefits. The
first is a reduction in size of approximately 2 to 1 relative to dual
proof mass designs. This not only reduces the size of the final sensor
chip but also increases the number of chips that can be arranged on a
single fabrication wafer. This last effect can greatly reduce the cost of
individual chips when produced in large quantities.
The use of only one proof mass also reduces power requirements needed to
vibrate the proof mass when compared to dual proof mass devices. Not only
is there less mass to move but there is no need for mechanical phase
controlling linkages between separate proof masses.
There are important performance benefits that stem from a single proof mass
design. These are related to the improved symmetry that can be achieved
for differential, dual mode operation. In particular, measurement errors
related to differences in proof mass temperature, vibration, and alignment
do not occur in a single proof mass device since these differences do not
exist.
2. Simplified Compact Design
The complexity of the suspension system shown in FIG. 1 differs from
earlier approaches in the number and shape of the flexures needed to
control proof mass and resonator motion. The MAC sensor uses fewer
flexures and does not require the high aspect etching techniques needed to
fabricate flexures that are long and narrow. As a result, the number of
lithography masks and the difficulty of the micromachining process is
reduced. The use of wide, short flexures also increases the strength of
the structure since material stresses are reduced for these geometries.
Another benefit of the MAC design is a simplification of the vibrational
modes inherent in the structure. The reduction in number and complexity of
the various flexures reduces the number and increases the frequency
separation of unwanted, parasitic modes. This reduces the effort needed to
design the structure and improves the overall measurement performance.
3. Perpendicular Dither Motion
The first embodiment of the MAC sensor differs from earlier devices in that
the dither motion of the proof mass is perpendicular to the wafer surface
instead of parallel. This allows for greater precision in alignment of the
forces that produce the dither motion and in the flexure structures that
control this motion.
Alternate approaches rely upon external parts, such as magnets and pole
pieces, that can effect the alignment of in-plane dither forces. These
external parts are sensitive to their mounting structures and can shift or
change due to handling and aging of the overall sensor assembly. These
effects are reduced in the MAC geometry since the electrostatic plates
that determine the perpendicular dither forces are an integral part of
each MAC sensor chip.
Another advantage of perpendicular motion relates to the isolation of
orthogonal modes of vibration. The frequency of the proof mass in the
perpendicular direction is much lower than the in-plane directions. This
means the isolation of these modes and the ability to eliminate unwanted
in-plane dither motion is improved.
4. Adjustable Electrostatic Drive Frequencies
Both the proof mass and resonators use electrostatic fields to produce
their vibrational motion. Since the exact frequency of an electrostatic
resonator can be adjusted by application of an external DC bias in these
fields, it is possible to fine tune the proof mass and resonator
frequencies after the sensor chip has been fabricated. This means that
slight variations in frequency or electronic response caused by
manufacturing tolerances can be corrected after fabrication. This is done
by adjusting the DC biases applied to the MAC chips by its external
electronics.
IV. Alternate Configurations of the First Embodiment
Outlined below are several alternative configurations of the first
embodiment of the MAC sensor.
A. All Silicon Sensor Assembly
The MAC sensor can be made from materials that are different than described
above. In particular, the Pyrex caps 24 and 25 could be made from silicon.
This would reduce the residual stresses caused by differences in thermal
expansion between Pyrex and silicon. While the use of silicon caps might
make the bonding and inspection of the chip more complicated, the design
is compatible with both materials and final material selection may be
dependent on the applications for which the chips is designed.
B. Single Axis Sensor
It is possible for the MAC chip to measure linear and angular motions
separately and to use the device as an individual accelerometer or
Coriolis rotation sensor. Since the ability to measure linear acceleration
is effected by the rotational measurement, it is possible to optimize the
measurement of one quantity at the expense of the other. This device is
compatible with those applications where separate acceleration and
rotation sensors of better performance are beneficial.
C. Four Axis Monolithic Sensor
The sensor geometry shown in FIG. 1 can be modified to produce a four axis
sensor as shown in FIG. 4. Such a sensor has the flexures 8, 9, 10 and 11
as shown in FIG. 1 replaced with additional resonators 29 and 30. It can
be seen from the symmetry of the chip that these additional resonators
would exhibit a measurement capability for linear accelerations in the y
axis and rotational velocities along the z axis. In this embodiment, one
chip would function as two accelerometers and two rotation sensors for
those applications where this would be beneficial.
D. Six Axis Monolithic Sensor
The MAC sensor could operate as a complete six axis sensor if modified as
shown in FIG. 5. This arrangement is similar to that shown in FIG. 4 with
the addition of new resonators 33 and 34. These resonators have been
positioned so that rotational acceleration about the x axis can be
measured.
In particular, a rotational acceleration about the x axis would add a
tensile stress to resonator 3 while producing a compressive stress in
resonator 33. This rotational acceleration could be measured by taking the
difference in the frequencies of these two resonators using the signal
processing techniques discussed above. Measuring the frequency difference
between resonators 29 and 34 would add to the sensitivity of this
measurement and contribute to the rejection of errors common to this mode
of measurement.
Measurements of linear acceleration along the x axis can be obtained by
making precise measurements of the proof mass dither signal. If a DC bias
voltage is applied between the proof mass electrodes on the chip caps 24
and 25, the average frequency of the proof mass becomes dependent on the
proof mass's equilibrium position. Since this equilibrium position is
effected by forces applied in the x direction, the linear acceleration
along the x axis can be determined from the average proof mass frequency.
In other words, measuring the reference frequency 19 coming from the proof
mass oscillator 12 can determine the linear acceleration in the x
direction.
V. Mechanical Design of a Second Embodiment
In a second embodiment of the present invention, a micromachined sensor is
provided for measuring linear and angular motion.
In one particular configuration, the sensor comprises a generally planar
substrate, excitation means for vibrating the proof mass at a dither
frequency, sensing means for sensing the vibration of the resonators, and
means for mounting the excitation means and the sensing means adjacent the
proof mass.
The generally planar substrate is generally aligned in a wafer plane
defined by a first axis and a second axis, wherein the second axis is
orthogonal to the first axis, wherein the substrate is generally
perpendicular to a third axis which is orthogonal to the wafer plane. The
substrate is formed to include: a frame or frame-like main body portion
having an inner cavity; a proof mass disposed in the inner cavity, the
proof mass having a top surface and a bottom surface; a flexural support
means for connecting the proof mass to the frame and suspending the proof
mass within the cavity; and a plurality of resonators, including at least
two opposite resonators which are disposed on opposite sides of the proof
mass.
The proof mass is capable of vibrating outside the wafer plane, and is
capable of applying linear acceleration and rotational Coriolis forces, or
displacements caused thereby, to the resonators in response to the linear
and angular motion of the sensor.
The plurality of resonators may include at least two offset resonators
which are disposed on different planes, the different planes being
generally parallel to the wafer plane. The plurality of resonators may
include at least two coplanar resonators.
The linear movement of the sensor along the third axis causes the proof
mass to modulate the resonant frequencies of the resonators, wherein the
vibration frequency around the natural resonant frequency of one of the
resonators increases while the vibration frequency around the natural
resonant frequency of an opposite resonator decreases, and wherein the
difference in vibrational frequency around the natural resonant frequency
between the resonators is proportional to the translation of the sensor
along the third axis.
The rotational movement of the sensor about the third axis creates Coriolis
forces which induce an oscillating torque on the proof mass about the
first axis, thereby causing the proof mass to modulate the frequency of
the resonators, wherein the vibration frequency of a first resonator is
increased while the vibration frequency of a second resonator decreases,
wherein the difference in vibration frequency of the first and second
resonators is proportional to the rotation rate of the sensor about the
third axis.
The means for vibrating the proof mass may include means for rotationally
dithering the proof mass about the second axis at the dither frequency.
The plurality of resonators may further comprise a first resonator disposed
proximate the top surface of the proof mass and generally along the second
axis, and a second resonator disposed proximate the bottom surface of the
proof mass and generally along the second axis.
The natural resonant frequencies of the resonators may be substantially
equal.
The mounting means may include a pair of caps, each cap having an inner
surface and an outer surface, wherein the inner surface is provided with a
well or recess, wherein the generally planar substrate is disposed between
the caps and attached thereto, and wherein the wells are adapted to allow
the proof mass to vibrate outside the wafer plane.
The means for vibrating the proof mass may further include: a plurality of
electrodes disposed in at least one of the wells and adjacent the proof
mass, the plurality of electrodes including at least one proof mass driver
electrode for providing electrostatic forces to the proof mass thereby
causing the proof mass to vibrate at the dither frequency; electronic
circuitry, connected to the plurality of electrodes, for exciting the
plurality of electrodes and for sensing modulations in the vibration
frequency of the plurality of resonators caused by the linear acceleration
and rotational Coriolis forces so as to produce acceleration and rotation
signals indicative of the linear and angular motion of the sensor; and
means for connecting the electronic circuitry to the plurality of
electrodes.
The plurality of electrodes may further comprise a plurality of proof mass
balance electrodes. The balance electrodes may further comprise a
plurality of diagonal balance electrodes.
The sensor may also include means for damping proof mass resonance about
the first axis in order to improve dynamic response. The proof mass
resonance damping means may include means for applying an oscillating
voltage to the electrodes.
The driver electrodes rotationally dither the proof mass about the second
axis at the dither frequency.
The means for connecting the electronic circuitry to the plurality of
electrodes may further include at least one electroplated feedthrough hole
disposed through at least one of the caps, wherein the feedthrough hole is
adapted to supply electrical energy to the electrodes.
At least one of the resonators may be a cantilever beam having a proximal
end attached to the proof mass and a free distal end extending into the
cavity.
The vibration frequency corresponding to the linear movement is modulated
about a frequency which differs from the dither frequency.
The sensor may further include means for decoupling the resonator modes of
opposed the resonators.
At least two of the resonators may have a frequency mismatch.
The sensor may be adapted to exhibit a diagonal inertia tensor, equal
rotational frequencies.
The flexural support means may further include a first plurality of opposed
flexural supports generally disposed in a first plane, wherein the first
plane is generally parallel to the wafer plane.
The flexural support means may further comprise a second plurality of
opposed flexural supports generally disposed in a second plane, wherein
the second plane is generally parallel to the wafer plane, and wherein the
second plane is offset from the first plane.
The flexural support means may further comprise a plurality of diagonally
opposed flexural supports. In one particular arrangement, the diagonally
opposed flexural supports total four supports. In another particular
arrangement, the diagonally opposed flexural supports total eight
supports.
The diagonally opposed flexural supports may be coplanar.
The sensor may include at least one body attached to the proof mass,
whereby the mass and at least one moment of inertia of the proof mass is
increased. The body may be bonded to the proof mass. The body may comprise
at least two opposing bodies attached to opposite sides of the proof mass.
In a particular arrangement, the body is generally spherical. The means
for mounting the excitation means and the sensing means adjacent the proof
mass may further include at least one throughhole adapted to allow at
least a portion of the body to extend therethrough.
The electronic circuitry may include a proof mass oscillator for exciting
the proof mass through the plurality of electrodes. The proof mass
oscillator may sense the first natural resonant frequency of the proof
mass and provide a reference frequency output relating thereto.
The electronic circuitry may also include resonator oscillator means for
exciting the resonators. The resonator oscillator means sense modulations
in the plurality of resonators and provides frequency modulated outputs
related thereto.
The electronic circuitry may further comprises demodulators for processing
the frequency modulated outputs and for providing linear acceleration
signals and rotational velocity signals.
The electronic circuitry may further comprise a differential synchronous
detector for processing the rotational velocity signals and for providing
differential rotational velocity signals.
Furthermore, the electronic circuitry may include a differential frequency
counter for processing the linear acceleration signals and for providing
differential linear acceleration signals.
The major elements of a particularly preferred second embodiment of a
device 50 according to the present invention are shown in FIGS. 6-10 and
includes a monolithic electromechanical structure that performs all the
sensor's mechanical functions. The structure includes a frame or
frame-like main body portion or a frame-like substrate 52, a vibrating
proof mass 54, two flexural resonators 56, and a set of flexural supports
58. The present invention may be embodied in various sensor
configurations. The structure is referenced to the right handed xyz
coordinate system shown in FIG. 10. The linear and rotational
sensitivities of the sensor are parallel to the z-axis and perpendicular
to the wafer plane. Nomenclature for the second embodiment can be found in
Table
TABLE 2
______________________________________
NOMENCLATURE FOR THE SECOND EMBODIMENT
A = electrode area
A.sub.r = resonator electrode area
a = proof mass length (y direction)
a.sub.z = acceleration (z direction)
a.sub.zmax
= maximum acceleration (z direction)
b = proof mass width (x direction)
b.sub.f = flexure width
b.sub.r = resonator width
c = proof mass thickness
E = silicon modulus of elasticity
.epsilon..sub.0
= dielectric coefficient
F.sub.pm
= force on proof mass
f.sub.bw
= bandwidth
f.sub.x = proof mass frequency about x axis
f.sub.y = proof mass frequency about y axis
f.sub.z = proof mass frequency about z axis
G.sub.d = gap at dither drive electrodes
.GAMMA. = moment of inertia ratio
I.sub.x = moment of inertia about x axis
I.sub.y = moment of inertia about y axis
I.sub.z = moment of inertia about z axis
k.sub.fz
= flexure stiffness in z direction
l.sub.f = flexure length
l.sub.r = resonator length
m.sub.bb
= mass of bottom proof mass ball
m.sub.bt
= mass of top proof mass ball
m.sub.pm
= mass of proof mass
m.sub.r = effective mass of resonator
n = number of flexures
.omicron..sub.x
= flexure separation along x axis
.omicron..sub.y
= flexure separation along y axis
.OMEGA..sub.z
= angular rotation rate about z axis
.omega..sub.z
= linear proof mass frequency along z axis (rad/sec)
.omega..sub.x
= angular proof mass frequency about x axis (rad/sec)
.omega..sub.y
= angular proof mass frequency about y axis (rad/sec)
Q.sub.x = proof mass resonance Q about x axis
Q.sub.y = proof mass resonance Q about y axis
r.sub.t = radius of top ball
r.sub.b = radius of bottom ball
.rho.b = ball density
.rho.pm = proof mass density
.rho.r = resonator density
s = proof mass electrode moment arm
t.sub.f = flexure thickness
t.sub.r = resonator thickness
.theta..sub.x
= proof mass rotation about output x axis
.theta..sub.y
= proof mass dither rotation about y axis
V.sub.d = proof mass dither drive voltage
V.sub.0 = electrode bias voltage
Z.sub.d = proof mass dither displacement
Z.sub.0 = proof mass Coriolis displacement at resonator
Z.sub.pm
= proof mass linear displacement
______________________________________
As best seen in FIGS. 6-9, the micromachined silicon wafer is preferably
bonded to two Pyrex glass or silicon caps 60. Both of these caps 60 have
proof mass wells or recesses 62 that are etched into the caps' surfaces.
These wells 62 are recessed an amount sufficient to allow for the
vibrational motion of the proof mass 54 perpendicular to the xy plane. The
wells 62 also contain metallic electrode patterns or drive and balancing
electrodes 64 that are used to vibrate the proof mass 54 and the
resonators 56. Electroplated feedthrough holes 66 are formed in the caps
60 to make electrical contact to the inside of the chip. These
feedthroughs 66 have topside electrode patterns that can be used for wire
bonding. For example, an upper Pyrex cap may support upper electrodes and
input/output wire bonding pads 68, a lower Pyrex cap may support lower
electrodes and chip mounting surfaces, and a wafer or silicon layer may
contain accelerometer and gyro structures.
A. Chip Design
The proof mass 54 consists of a central plate 70 of single crystal silicon
that is bonded to two precision silicon nitride spheres 72, which is
unique to the second embodiment of the present invention and is a critical
fabrication step in producing this type of sensor. These spheres 72 offer
several benefits, including up to at least a twenty-five times increase in
the rotational sensitivity of the structure because the microspheres add
structural height to the silicon wafer 70, thereby improving its moment of
inertia properties. These microspheres 72 also add additional mass to the
proof mass 54 which increases the overall accelerometer sensitivity. The
microspheres 72 may be attached by bonding techniques similar to surface
mount die bonding and indium compression seals, or by both compression and
solder-based bonding. The central plate 70 may be provided with a
microsphere alignment recess 74 to facilitate placement of each sphere 72.
Another critical fabrication process step deals with the balancing of the
proof mass assembly after sensor fabrication. Since the device 50 is a
coupled, dual-mode Coriolis sensor, it is sensitive to cross-axis proof
mass motions that occur in unbalanced vibrating systems. In particular,
variations in the mass/stiffness symmetry of the device 50 can contribute
to the bias of the rotational velocity measurements. While these
variations are impossible to eliminate in any real physical system, they
can be minimized by adjusting the mass distribution of the proof mass 54.
This can be accomplished by laser trimming mass from flexures, the proof
mass, and the silicon nitride microspheres. These spheres 72 are directly
accessible through central holes 76 in the top and bottom caps 60 and can
be adjusted to improve the static and dynamic balance of the proof mass
54. Additional adjustments to the sensor's balance are made after laser
trimming by controlling the electrostatic bias voltages applied to the
metallic electrodes 64 mounted above and below the proof mass 54. This two
step method of controlling proof mass balance will significantly reduce
the cross axis coupling that ultimately contributes to measurement bias.
More than one micromachined sensor may be fabricated simultaneously on a
single crystal silicon wafer. The wafer is fabricated using bulk
micromachining techniques. After heavy p-type diffusion (later used as a
substrate contact), a deep anisotropic etch from the frontside is used to
set the resonator 56 and flexure 58 thickness on the bottom surface to
between 10 and 20 microns. A second anisotropic etch from the backside
likewise sets the thickness of the frontside resonator 56 and flexures 58.
Isotropic plasma etches are then used to form the resonator and flexure
shapes from the diaphragm regions left by the deep etches and to free the
proof mass 70 from the frame 52. The single crystal silicon wafer is
subsequently bonded to two Pyrex cap wafers 60 to form a three part
sandwich assembly. Recesses 76 are formed in the Pyrex caps using
hydrofluoric acid and gold electrodes are sputtered, patterned, and
etched. This metalization forms the substrate contacts during anodic
bonding as well as the electrode patterns used to drive and sense
resonator motion. Since the metal traces run entirely on the glass
surface, any stray capacitance between traces and to the substrate are
minimized.
The anodically bonded three layer sandwich assembly is then diced into the
individual microchips. Each chip contains all the mechanical parts needed
for a complete sensor stage. These chips are then assembled along with
their associated electronics into sensor packages. A six degree of freedom
inertial measurement unit is comprised of three chips with their support
electronics. The chips are oriented in a way for each of three orthogonal
axes of rotation and acceleration to have a non-zero projection onto at
least one of the sensing axes of the chips.
Referring to FIGS. 7-9, one particular embodiment of the present invention
was constructed having a 10 mm width, 10 mm length, and 1.5 mm depth
wherein the spacing 80 between feedthrough holes or corresponding bond
pads was 2.54 mm, and further included two 1.0 mm diam-gold plated silicon
nitride spheres.
FIG. 10 shows two spheres attached to a proof mass means having a plurality
of flexures and resonators, illustrated without attachment to the
remainder of the substrate or the caps.
VI. Principles of Operation of the Second Embodiment
The sensor of the second embodiment of the present invention is a highly
integrated device that provides for the simultaneous, differential
measurement of linear and rotational motion using only one monolithic
proof mass 54. This multiplicity of functions is achieved by controlling
and monitoring several different modes of proof mass motion
simultaneously. To explain the sensor's operation, the effects of linear
and rotational motions on the proof mass will be described separately.
A. Linear Acceleration
The prime function of the proof mass 54 is to generate microscopic motions
that are related to the inertial motion of the sensor and can be sensed by
the resonators 56.
One of these motions is produced by acceleration in the z direction as
shown in FIG. 11 by the simplified illustration of a proof mass including
two spheres and two resonators. When the substrate is accelerated along
this axis, the inertia of the proof mass 54 produces a counterforce that
moves the proof mass in the z direction.
In one particular embodiment, for example, changes in proof mass frequency
due to such acceleration may be approximately 2000 Hz.
It is shown herein that the resonant frequency of the sensor's resonator is
modulated by small changes in the position of the proof mass 54. As a
result, both resonators 56 will change their resonant frequency as the
proof mass 54 moves. The resonators 56 are positioned on opposite surfaces
of the proof mass 54 so that a motion of the proof mass in the positive z
direction (FIG. 10) will cause one resonator to increase its frequency
while the frequency of the other resonator will decrease. These changes in
resonant frequency will occur at the same rate as the applied acceleration
and will be proportional to the magnitude of this acceleration. In one
particular example, one resonator will exhibit a change in frequency of
about 2 kHz relative to its natural resonant frequency of 100 kHz when
subjected to an acceleration of 50 g.
The measurement of this acceleration is completed by subtracting the
frequency of one resonator from the frequency of the second resonator and
multiplying by a constant, predetermined scale factor. For example, a 50 g
acceleration may produce a total dual-stage differential frequency change
of more than 4 kHz. This simple operation provides a sensor output that is
highly linear and relatively free of common mode measurement errors caused
by temperature, aging, and electronic voltage drift.
B. Rotational Velocity
The Coriolis "force" is actually an apparent acceleration attributed to a
body that is in motion with respect to a rotating coordinate system. If
the proof mass is vibrated about the y axis in the simplified illustration
of FIG. 12 and, if the sensor substrate is rotating about the z axis, then
Coriolis forces will be produced that create an oscillating torque about
the x axis. The directions of these various motions, forces, and torques
are shown in FIG. 12.
The Coriolis forces oscillate at the frequency of the proof mass
y-rotation. This motion is called the proof mass "dither". The torque that
is created by the Coriolis forces also oscillates at the dither frequency
and produces a vibration about the proof mass' x axis that is proportional
to the rotation of the sensor about the z axis. This x axis motion is
detected by the sensor resonators using the same positional sensitivities
that enabled the detection of the linear z axis motion. In particular,
small changes in the proof mass angle about the x axis produce changes in
the resonant frequencies of the resonators. These changes occur at the
frequency of the dither motion and, therefore, produce a frequency
modulation of the resonators. The magnitude of this modulation is
proportional to the z axis angular velocity. In one particular example,
the magnitude of the modulation was about 400 Hz at each resonator when
the sensor was subjected to a rotation of 1,200.degree./s.
The feature of the Coriolis motion that distinguishes it from the linear
motion is its frequency. Since the Coriolis forces oscillate at the dither
frequency, they can be demodulated electronically to isolate this signal
from the lower frequency acceleration signal. The details of this
demodulation are described below. The phase of one of the demodulated
output signals is shifted by 180.degree. to create a differential,
dual-stage output for the rotational measurements that provides the same
benefits attributed to the linear acceleration measurements.
C. Temperature
The temperature of the sensor can also be obtained from its resonator
output frequencies. This is accomplished by adding the carrier frequencies
of each resonator and multiplying by the appropriate scale factor.
VII. Unique Features of the Second Embodiment
The present invention offers a unique design that has several inherent
advantages. Advantageous features stem from the geometry of the suspension
system used to support the proof mass and the use of vibrating resonator
beams to detect proof mass motion.
1. Single Proof Mass Design
The fact that only one proof mass is needed to produce differential outputs
for both linear and rotational measurements offers several benefits. The
first is reduction in size of approximately 2 to 1 relative to dual proof
mass designs. This not only reduces the size of the final sensor chip but
also increases the number of chips that can be arranged on a single
fabrication wafer. This last effect can greatly reduce the cost of
individual chips when produced in large quantities.
The use of only one proof mass also reduces power requirements needed to
vibrate the proof mass when compared to dual proof mass devices. Not only
is there less mass to move, but there is no need for mechanical phase
controlling linkages between separate proof masses.
There are important performance benefits that stem from a single proof mass
design. These are related to the improved symmetry that can be achieved
for differential, dual mode operation. In particular, measurement errors
related to differences in proof mass temperature, resonator
nonlinearities, vibration, and alignment do not occur in a single proof
mass device as these differences do not exist.
2. Simplified Compact Design
The complexity of the suspension system of the second embodiment shown in
FIGS. 6-10 differs from other approaches in the number and shape of the
flexures needed to control proof mass and resonator motion. The sensor
uses fewer flexures and does not require the high aspect etching
techniques needed to fabricate flexures that are long and narrow. As a
result, the number of lithography masks and the difficulty of the
micromachining process are reduced. The use of wide, short flexures also
increases the strength of the structure since material stresses are
reduced for these geometries.
Another benefit of the present design is simplification of the vibrational
modes inherent in the structure. The reduction in number and complexity of
the various flexures reduces the number and increases the frequency
separation of unwanted, parasitic modes. This reduces the effort needed to
design the structure and improves the overall measurement performance.
3. Out-of-Plane Dither Motion
The present invention differs from other devices in that the dither motion
of the proof mass is perpendicular to the wafer surface instead of being
parallel. This allows for greater precision in alignment of the forces
that produce the dither motion and in the flexural support means or
flexure structures that control this motion.
Alternate approaches rely upon external parts, such as magnets and pole
pieces, that can affect the alignment of in-plane dither forces. These
external parts are sensitive to their mounting structures and can shift or
change due to handling and aging of the overall sensor assembly. These
effects are reduced in the present geometry since the electrostatic plates
that determine the perpendicular dither forces are an integral part of
each chip.
Another advantage of perpendicular motion relates to the isolation of
orthogonal modes of vibration. The frequency of the proof mass in the
perpendicular direction is much lower than the frequencies in the in-plane
directions. This means the isolation of these modes and the ability to
eliminate unwanted in-plane dither motion is improved.
4. Adjustable Electrostatic Drive Frequencies
Both the proof mass and resonators use electrostatic fields to produce
their vibrational motion. Since the exact frequency of an electrostatic
resonator can be adjusted by the application of an external dc bias in
these fields, it is possible to fine-tune the proof mass and resonator
frequencies after the sensor chip has been fabricated. This means that
slight variations in frequency or electronic response caused by
manufacturing tolerances can be corrected after fabrication. This is done
by adjusting the dc biases applied to the sensor chips by its external
electronics.
VIII. Alternate Configurations of the Second Embodiment
The sensor can be made from materials that are different than those
described above. In particular, the Pyrex caps could be made from silicon,
which would reduce the residual stresses caused by differences in thermal
expansion between Pyrex and silicon. While the use of silicon caps might
make the bonding and inspection of the chip more complicated, the design
is compatible with both materials, and final material selection may be
dependent on the applications for which the chip is designed.
In addition to the embodiment shown in FIGS. 15-18, other embodiments may
have the same or similar relative positioning of flexures and resonators,
wherein all of those features are disposed in a single plane. It is
expected that these other embodiments may not perform as well as those
similar to that shown in FIGS. 15-18, however the other embodiments may
require substantially fewer fabrication steps and hence lower cost.
IX. Analysis of the Second Embodiment
1. Accelerometer Analysis
Estimates of the accelerometer scale factor can be made by using a simple
linear spring mass model. The deflection of the proof mass in the z
direction caused by linear acceleration can be calculated using Newton's
second law of motion combined with Hooke's law of elasticity.
##EQU6##
These equations show that the deflection of the proof mass can be
calculated when the resonant frequency of the proof mass is known. The
resonant frequency can be calculated from calculated proof mass and
flexure dimensions. The maximum deflection of the proof mass, when
subjected to a maximum acceleration is, therefore:
##EQU7##
This is the maximum deflection that needs to be measured by both
resonators when the sensor is subjected to the maximum acceleration. Note
that this deflection should be smaller than the resonator's electrode gap.
The change in resonator frequency caused by this deflection is given by:
.DELTA.f.sub.a =.epsilon..multidot.f.sub.0 .multidot.z.sub.pm[ 39]
The natural resonant frequency of a single cantilever beam is determined
from:
##EQU8##
The gap sensitivity can be calculated from:
##EQU9##
Combining these equations with the estimate of proof mass deflection leads
to:
.DELTA.f.sub.a =.epsilon..multidot.f.sub.0 .multidot.z.sub.pm[ 42]
which gives a single stage scale factor of:
##EQU10##
and a dual-stage scale factor of:
dual-stage scale factor=2.multidot.k.sub.a [ 44]
2. Gyro Analysis
The response of the gyro channel is determined by calculating the coupling
of the y axis dither motion into the x output axis as created by the
rotationally induced Coriolis forces. This cross-axis coupling can be
visualized using equivalent mass and moment "sphere and stick" model shown
in FIG. 13.
FIG. 13 shows how the dither velocity of the z axis spheres, combined with
inertial rotation about the z axis, creates a torque about the x axis.
This torque produces a rotation about the x axis that is given by
##EQU11##
where
##EQU12##
Note that the magnitude of the x axis rotation is proportional to the
angular velocity about z. The x axis rotation creates a displacement o f
the y axis spheres in the z direction. Since the y axis dither motion is a
vibration of a given frequency, the resulting output motion is also
vibrational at the same frequency. This motion is sensed by the resonators
located at the equivalent positions near the ends of the proof mass.
3. Proof Mass Calculations
Equation 45 shows that the ratio of proof mass moments denoted by .GAMMA.
is a critical factor in the cross coupling of resonator modes. Since the
angular response of the sensor is proportional to .GAMMA., it is important
to increase the value of this term as much as possible. Analysis of this
term shows that its magnitude increases as the height of the proof mass
grows in the z direction. This is difficult to accomplish through
conventional planar micromachining methods and is the prime reason the
precision silicon nitride spheres have been added to the structure in this
embodiment.
The value of .GAMMA. can be calculated from the moments of inertia of the
combined double sphere proof mass geometry. Removal of the spheres could
reduce the value of .GAMMA. by two orders of magnitude, e.g. from 1.1 to
0.04. Thus, the spheres contribute significantly to the magnitude of the
proof mass mode coupling and can substantially increase the response of
the sensor. The double sphere proof mass design is a unique advantage of
the present invention.
4. Mode Analysis
A finite element analysis (FEA) was performed for a particular
configuration of the second embodiment to characterize the operational
modes of the proof mass in order to optimize the linear and rotation rate
scale factors and also to identify parasitic modes that could interfere
with the operation of the device. By its nature the analysis was
iterative. Implicit in an FEA calculation was the computation of the
moments of inertia and flexural properties of the silicon struts. The FEA
demonstrated that dimensions for the proof mass, resonators, and flexures
fully compatible with this fabrication technology do give gyro and
accelerometer responses described below. Isolation of parasitics from the
operational linear and rotational modes was also demonstrated.
5. Proof Mass Drive and Balance Electrodes
The dither drive system shown in FIG. 14 is designed to oscillate at the
natural resonant frequency of the y axis. This becomes the reference
frequency for all sensor functions. The resonant frequencies of the y
(dither) and x (Coriolis) modes are approximately the same. This near
equality enhances the gyro scale factor. However exact equality is not a
critical requirement since amplitude and phase variations caused by slight
imbalances in these frequencies are accounted for by the sensor
electronics. The x axis damping circuit shown in FIG. 14 compensates the
sensor for the x axis frequency offsets and provides a reduction in x axis
Q needed to maintain the sensor's bandwidth. The details of the sensor's
gain/bandwidth trade-offs is described in the section below.
Electrostatic balancing is accomplished by applying biases to the drive
electrodes as well as the set of eight diagonal balance electrodes shown
in FIG. 14. This array of balancing electrodes is designed to trim out
flexural and mass imbalances introduced during the silicon layer
fabrication as well as misalignments of the drive electrodes to the proof
mass. These imbalances and misalignments could lead to biases that
interfere with detection of the inertial signals the sensors are designed
to monitor. The goal of electrostatic balancing is to reduce these biases
consistent to specifications such as those found in Tables 3 and 4 below.
The biases applied to the dither drive electrodes are used to correct for
net stiffness difference between the top and bottom flexures, net
stiffness variation that would give a non-zero y-z component to the
compliance matrix (k.sub.yz), and differences in the diagonal compliances
that would move the dither and the Coriolis modes off-resonance.
Similarly biases on the x electrodes are used to correct for top to bottom
stiffness imbalance and buck out k.sub.xz off-diagonal terms. Diagonal
balance electrodes trim out k.sub.xy and electrode misalignment about the
proof mass z-axis.
By way of example, in one particular embodiment of the present invention, a
dither drive was set at 28V yielding a Q of 1000 at 75V, a damping drive
was set at less than 0.5V yielding a Q of 20 at 75V, a resonator drive was
set at approximately 0.05V yielding a Q of 50,000 at 20V, and a balance
offset was set at less than 100V, plus or minus 1 micron flexure
tolerance.
6. Dither Drive Calculations
Equation 45 shows that the output motion is also proportional to the
magnitude of the dither motion. This dither motion is generated using the
system shown in FIG. 14. Differential equations of motion that describe
the y axis motion of the proof mass (subjected to the dither drive
electrostatic forces) show that the magnitude of this motion is:
##EQU13##
which is the displacement at the sides of the proof mass.
Since the overall response of the gyro channel is proportional to this
displacement, the magnitude of the dither drive is held constant by an
automatic gain control loop contained in the dither oscillator. This gain
loop accounts for changes in dither drive amplitude created by changes in
Q or electronic phase shifts and maintains control of the gyro's output
scale factor.
In one particular example, a y axis Q of 1,000 was used to estimate dither
deflection, which was conservative relative to typical proof mass Q's of
10,000 and 12,000. If the proof mass exhibits Q's of this magnitude after
fabrication, the levels of the dither drive voltages can be reduced
accordingly. For reasons relating to sensor bandwidth, it is desirable to
limit the Q.sub.x of the x axis rotation. This is done electronically by
applying an oscillating voltage to the proof mass electrodes that are
symmetrical with the x axis. This oscillating voltage has an amplitude and
phase that is proportional to the x axis velocity and, therefore, produces
an equivalent damping force that limits the x axis Q.sub.x. The generation
of this damping voltage is discussed below.
7. Scale Factor/Bandwidth Analysis
The above calculations can be used to evaluate the sensor's rotational
scale factor. Equation 45 can be modified to calculate the proof mass
deflection at the resonators that is caused by substrate rotation.
##EQU14##
This can be further modified by the following relationship:
##EQU15##
to show the explicit relationship between proof mass motion and output
bandwidth:
##EQU16##
The proof mass motion z.sub.0 modulates the resonators' natural resonant
frequencies at the dither drive frequency. Equation 42 can be used to
calculate the magnitude of this modulation, or the change in resonator
frequency caused by the rotationally induced Coriolis force.
The estimated single-stage rotational scale factor is:
##EQU17##
A dual-stage scale factor is double the single-stage scale factor. Thus, a
magnitude of modulation is achievable which is easily measured by the
sensor electronics and provides an angular signal response that is well
balanced with respect to the signal response of the acceleration channel.
This estimated scale factors response is a critical value used to estimate
additional sensor parameters.
Equation 49 can also be used to calculate the Q.sub.x needed to meet scale
factor and bandwidth requirements. The proof mass resonance about the x
axis is:
##EQU18##
Since the bandwidth of the sensor is inversely proportional to Q, the
response of the sensor would be reduced in time if Q.sub.x is allowed to
reach this value. Although a large Q would increase the magnitude of the
sensor's response, the time needed to respond to a given input would also
increase. As a result it may be necessary to limit the value of Q.sub.x by
providing an electronic damping signal. This signal, generated from
amplitude and phase information determined in the sensor's digital signal
processing system, is applied to the x axis proof mass plates to add to
the coordinate's damping.
X. Performance Estimates of the Second Embodiment
Estimates of the performance of the second embodiment of the present
invention constructed according to a particular set of design parameters
are shown in Tables 3 and 4. These estimates are based upon data related
to one particular set of requirements and upon the above sensor analysis.
Of course, other performance values are possible with certain design
modifications.
TABLE 3
______________________________________
ACCELEROMETER PARAMETERS
Estimated
Accelerometer Sensor
Parameters Units Performance
______________________________________
Bias Stability
micro-g (1 sigma)
300
Random Walk m/s/.sqroot.h
0.02
Axis Misalignment
micro-rad (1 sigma)
150
Scale Factor Error
ppm (1 sigma)
180
Frequency Response
Hz 300
Linear Range g 50
______________________________________
TABLE 4
______________________________________
GYRO PARAMETERS
Estimated
Sensor
Parameter Units Performance
______________________________________
Bias Drift Rate .degree./h (1 sigma)
1.4
Angle Random Walk
.degree./.sqroot.h (1 sigma)
0.15
Axis Misalignment
micro-rad (1 sigma)
100
Axis Repeatability
micro-rad (1 sigma)
170
Scale Factor Error
ppm 200
Minimum Bandwidth
Hz 300
Maximum Rate Capability
.degree./s .+-.1,200
______________________________________
A good estimate of sensor performance can be obtained by calculating the
response of the linear and rotational channels. Once the individual scale
factors have been determined, the performance of other sensor parameters
can be scaled from the known performance of similar devices.
XI. Resonator Modes
FEA analysis showed a coupling between the two opposed resonators due to
the finite mass of the proof mass. This coupling could lead to
non-linearities in the gyro and accelerometer scale factors. To avoid this
the resonators may be designed with a slight frequency mismatch.
The resonator modes themselves will likely show a statistical spread due to
inherent imperfections in the fabrication process. Resonator modes that
lie near parasitics will have low Q and not function optimally or at all.
For this reason resonators may be designed to position their mode
frequencies midway between parasitics, in modal clear windows, in order to
maximize die yield on the wafer.
XII. Alternate Sensor Designs for the Second Embodiment
The fabrication process allows variations on the above design to be
manufactured on the same wafer. As shown in FIGS. 15-18, the
configurations may differ in the details of the resonators and proof mass
suspension system. For example, FIGS. 15 and 16 show low and high band
resonator variations, respectively. FIG. 17 shows an eight-flexure sensor
design. FIG. 18 shows a coplanar flexure/single microsphere sensor.
All four embodiments shown in FIGS. 15-18 exhibit a diagonal inertia
tensor, equal rotational frequencies about the x and y axes, and
symmetrically patterned electrostatic driver and balance electrodes.
As seen in FIGS. 15, 16 and 18, three of the configurations have four
diagonally opposed silicon flexures. This arrangement allows thermal
stresses transmitted from the pyrex caps to the flexures to be relieved
through a slight rotation of the proof mass perpendicular to the z axis.
The rotation gives rise to a temperature dependent gyro bias that can be
included in the overall error budget.
An anodically bonded glass-silicon interface may exhibit elastic
properties. The eight flexure design illustrated in FIG. 17 should exhibit
much greater thermal scale factor and bias sensitivities. The caps may be
fabricated on the same wafer, and silicon caps in place of pyrex may
reduce the effects of thermal sensitivities in certain embodiments.
The coplanar flexure/single microsphere design of FIG. 18 puts onto the
same plane both the principal flexure axes of the suspension system and
the center of mass of a proof mass/single microsphere assembly. The
two-microsphere, or dual microsphere, designs have the center of mass at
the silicon layer mid-plane, causing the flexures to exhibit lateral
motion as the proof mass is rocked about x and y. In other words, for the
non-coplanar designs, the dither and coriolis rotational modes have a
translational component along the x and y-axes, respectively. These
translational components may stiffen the mode frequencies and afford an
opportunity for the operational modes to couple with higher frequency
parasitics. This coupling should be small because of the mode separation.
For the dual microsphere designs, etch pits and a slight offset of the
microsphere placement wells may be used to mass balance the asymmetrically
etched resonator well and diagonalize the inertia tensor. The coplanar
flexure design does not require etch pits, rather the focus is on the
placement well for the microsphere which is designed to provide the right
insertion depth for the sphere to bring the center of mass up to the top
surface.
It will thus be seen that the objects set forth above, among those
elucidated in, or made apparent from, the preceding description are
efficiently attained and, since certain changes may be made in the above
construction, without departing from the scope of the invention, it is
intended that all matter contained in the above description or shown in
the accompanying drawings shall be interpreted as illustrative and not in
a limiting sense.
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